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Most Yield Curve analyses are based on par curves and/or zero-coupon curves. Placing trading positions based on par curves creates exposure across the entire yield curve up to the term of the traded instrument. The use of Treasuries (Bonds, Notes, Bills, Zeroes, etc.) and Vanilla IR swaps may be undesirable when the intended position is meant to profit from an expected change in a forward section of the yield curve.

The availability of Eurodollar futures goes a long way in solving this problem and allows a trader to place bets on his view of expected forward 3-month Libor rates. At this time, Euros are traded out to 10 years, though only the contracts out to five years are relatively liquid.

Previously, to place yield curve trades required the use euro futures combined with spot and forward swaps. These trades were restricted to funds with access to the swap market. Trades could be placed using Treasury Bond futures but with the risk of swap spreads fluctuating. With the advent of IR Swap futures a few years ago, yield curve trades became accessible to the retail investor. It is now possible for virtually anybody to place positions with a view of likely changes in the shape of the yield curve.

As mentioned earlier, there has been a lack of a common yield structure to analyse and view curves, trades and potential profit/losses. An alternative method uses the concept of continuous forward rates. This method has the advantage of allowing us to express the effective interest rate portions of the yield curve which is being placed long/short when entering into a fixed-income instrument transaction. It also produces a more pronounced description of forward yields with a richer structure that may be hidden when solely depending on par or zero curves.

My trading strategies are based on an instantaneous forward rate curve built using the Eurodollar futures strip combined with the 5, 10 and 30yr USD Interest Rate Swap futures contracts. Since the Euros trade out up to 10 years, the 5 and 10 yr Swap futures are simply used to confirm the robustness of the curve construction. The 30yr Swap futures price is used to fit the curve from 10yrs out to 30yrs.

The ongoing interventions by the Fed in maintaining an almost zero-rated short rate while buying back treasuries across the longer term periods has created an extremely humped forward curve. A similar shaped forward curve was seen in the Japanese market in the early 1990s when the Japanese injected liquidity into its bond market by bringing its short-term lending rate virtually to zero for an extended period of time. This humped forward curve remained for over five years allowing a relative value trade to earn a regular “carry” income while waiting for the forward curve to return to a normal shape. This profitable trading opportunities created by the humped shape will eventually force the curve to return to a normal shape. The longer it takes for the shape to normalize, the longer we can continue earning the trade’s “carry” income.

The downside to the trade is that a trader needs to remain cautious when putting on the intended position as market interventions may continue to make the curve even more humped. This situation creates even more profitable trading opportunities, but may force the trader out of his position if he has under-allocated margin resources to sustain intermediate losses. In case the curve becomes more humped and the position sustains some losses, the beneficial consequences are that the “carry” income will increase as well as the eventual profit that will be made when the curve normalizes.

There are various trading techniques and money management methods which can be used to minimize the chances of being forced out of the trade while balancing the profitability of the trading opportunity.

With this analysis system, I am able to build forward rate curves calibrated to euro prices and swap futures prices. Different portfolios consisting of euro and swap futures positions can be analysed for their carry income, potential profit upon reversion to a normal curve as well as maximum potential intermediate loss. Keep in mind that a loss on a yield curve carry / reversion trade leads to a greater carry income and a greater potential profit upon reversion.

Technical Description of Forward Curve Analysis System

My system assumes a step continuous forward rate curve fitted to Eurodollar prices having adjusted for futures vs forwards. The forward curve out from 10yrs to 30yrs is smoothly fitted by a cubic spline calibrating to the 30yr swap futures price. The 5yr and 10yr curve implied swap prices are computed and compared with the swap futures prices. The 5yr swap rates fit within 2-3 bp and the 10yr swap rates fit within 5-10 bp. This is well within bid offer spreads of the euros and swap futures not any possible arbitrage. Of course the 30yr implied swap futures price fits exactly, as it has been used for calibration of the curve.

The forward curve is nudged by a continuous 1bp move upward per forward date interval matching the euro future 3mo periods. The sensitivities of the Euro future contracts as well as the swap futures contracts are calculated.

I have also built a theoretical curve model to analyse the impact on portfolio positions of various curve shifts, i.e. reversion of the forward curve to a normal curve, diversion to a more severely humped curve, etc. This allows for the analysis of various portfolio strategies and how one could maximize carry income, profit from curve reversion or minimize possible loss from curve diversion, etc.

I have developed a simple system of computing the portfolio exposure graphically versus the yield curve to aid in trading strategy analysis.

These models and spreadsheets are in the development stage, therefore I would like to apologize for their lack of elegance and lack of usability and user protection. A few sample pages of the spreadsheets have been attached.

I welcome any further discussion regarding any of the calculations, techniques and assumptions used in the development of these systems and the application of the same to yield curve trading strategies.